An important aspect of battlefield intelligence is the real time assessment of the strength and disposition of the opposing force's mortar, artillery, missiles and rockets. To direct counterfire it is desirable to type the weight of these projectiles as light, medium or heavy. The weight of a projectile can be extracted from radar data utilizing the description of the projectile's acceleration a embodied in Equation (1), EQU a=-K.sub.D.rho..vertline..nu.-w.vertline.(.nu.-w)+g-2.omega..times..nu., (1)
and in particular the properties of the drag parameter K.sub.D. The other quantities and terms in equation (1) are air density .rho., projectile velocity .nu., wind velocity w, gravitational acceleration g, and Coriolis acceleration 2.omega..times..nu..
Equation (1), which represents the vector particle momentum or point mass (PM) approximation to the six degree-of-freedom model of the projectile's motion, accurately describes the flight of projectiles at lower quadrant elevations, with the caveat that rockets and missiles are in the rockets or missiles unpowered phase. Equation (1) is incorporated into radar tracking filters as the signal or plant model to obtain filtered position, velocity and acceleration estimates from raw measurement data. Equation (1) is also used in estimators extracting projectile time-of-flight (TOF), initial firing point and impact point from the tracking filter outputs. In carrying out these extraction and smoothing operations, the drag parameter represents another unknown that must be estimated from noise corrupted radar measurements. Because the drag parameter must be found to accomplish these radar track functions, it is natural to attempt to use the drag parameter to satisfy ancillary analysis requirements, such as projectile light, medium and heavy classification (LMH Class). This is done by associating the estimated drag parameter with one of a stored set of zero-yaw drag parameters with the set representative of all projectiles the radar will encounter.
FIG. 1 through FIG. 3 illustrate this approach of estimating the drag parameter. FIG. 1 illustrates a family of zero-yaw drag curves 100 characterizing 105 mm (curve 101), 155 mm (curve 106), 175 mm (curve 108), and 8 in (curve 104) artillery shells with the x-axis representing velocity, Mach number and the y-axis representing drag functions (K.sub.DO).times.10.sup.5 (-kg/meter.sup.2). In this example the 155 mm (curve 106) is considered medium weight: hence projectiles characterized by drag parameters lying above curve 106 are classed as light (e.g., curve 101), and those below (e.g., curve 108) are considered heavy. The family of curves 100 are represented as functions of the projectile Mach number (x-axis), and would typically be stored in lookup tables. To perform LMH-Class, the radar-tracking filter produces a velocity, from which, for example, Mach number 102 is derived which lies between Mach number 1.2 and 1.4. Associated with this Mach number 102 is the drag parameter estimate 103 from the tracking filter which lies below a drag function of 8.0. This drag parameter estimate 103 is closest to curve 104, and hence is associated with the 8 in projectile, so the projectile producing the track data is "heavy".
The drag parameter estimate is typically derived by the radar tracking filter using the concepts embodied in Pearce "A Universal Drag Curve for an Artillery Locating Radar," U.S. Army Electronics Command, Fort Monmouth, N. J. Technical Report ECOM 4088. Pearce showed that if each curve in FIG. 1 is normalized by its value at Mach 1.1, the family of curves 100 collapses as illustrated in FIG. 2 to the family of curves 200. Again in FIG. 2, the x-axis represents velocity--Mach number and the y-axis represents drag function (K.sub.DO).times.10.sup.5 (-kg/meter.sup.2). This new set of curves is essentially represented by a single curve 201. Pearce's normalization indicates that the shape of the drag curve for geometrically similar projectiles is known a priori and hence can be functionalized and incorporated into the tracking model based on Equation 1. Estimating the drag parameter in the tracking filter is then reduced to estimating a single constant which translates the single universal curve 201 representative of 200 to the appropriate curve in the set 100. Because estimating this scaling parameter from noise corrupted radar data is a highly nonlinear process, there is always a not negligible error associated with the result. This error was indicated in FIG. 1 by the estimate 103 not lying on the curve 104. But there is also a further error in the LMH-Class process that has not been addressed yet, and that is the error involved in going from the estimated velocity to the corresponding Mach number. This transformation involves meteorological measurements, and in particular measurements of wind speed and direction, air temperature and atmospheric pressure which may be hours old, or not available to the radar tracker at all.
The effect of errors in both drag parameter estimation and in Mach number is illustrated in FIG. 3. Because of meteorological and radar measurement errors, the Mach number associated with the drag parameter estimate 103 is not 102, but point 300 depicted in FIG. 3 at approximately Mach number 1.4. This translates the drag parameter estimate to the right from point 103 to point 301, which causes it to be incorrectly associated with the 155 mm curve (since difference 303 is smaller than difference 302), and hence falsely identified (IDed) or classified as belonging to a medium weight projectile. Difference 303 is the y-axis difference between the 155 mm curve and the point 301. Difference 302 is the y-axis difference between the 8-inch curve and the point 301.
Errors in estimating the drag coefficient, errors in estimating projectile velocity, and errors in meteorological data measurement do not have a significant impact on the use of Pearce's universal curve approach in the radar tracking filter, i.e. in generating projectile kinematics. But the impact of these errors make its use in extracting LMH-Class difficult, since typically an unacceptably high probability of false ID results. In fact, these errors impact any conventional approach that derives LMH-Class from drag estimates. Such approaches also suffer from the requirement of an extensive database, since every projectile encountered must have a drag parameter curve associated with it.